Applications Of DNA computing

1. Applications Of DNA computing By Anesu Chaora Bayo Olowoyeye

2. Introduction • Making DNA Add • Cryptography • Substitution • XOR • Steganography • Conclusion

3. Making DNA Add • DNA computing • Feasible for combinatorial problems like Hamiltonian Path Problem and NP-complete problems • Not feasible for simpler problems • The design of a versatile computer requires development of the bit manipulations for carrying out addition

4. Adding • Mathematical calculations such as addition represent a different problem than the solution of search problems • A search problem can be solved by generating all possible combinations and searching for the correct output • Binary operations such as addition require that only the correct output is produced in response to specific inputs. • Requires a different model for use of DNA computing that that used previously for search procedures.

5. General Algorithmfor Adding • Begin with the DNA representation of all pairs of input. Nonnegative two-digit integers. • All DNA sequences are single-stranded, unique and non-complimentary, except of overlining DNA sequences. For example: ____ DEF(0, 1) is complimentary to DEF(0, 1)

6. DNA representation of all possible nonnegative two-digit binary integers

7. Binary addition 11 + 10

8. Adding • These successive reactions together represent an example of a process called a horizontal chain reaction. • This is a process in which input DNA sequences serve as successive templates for extension of a result strand. • In our example our resulting strand encodes three digits, including operator sequences that represent precisely and in the correct order the outcome of the addition operation. Result being 100

9. Generalization of the Algorithm • The generalization of this algorithm to the addition of two nonnegative n-digit binary numbers is straightforward. • If necessary 0s are added to the left of smaller integers, so both numbers can be represented by the same number of digits. • The two digits in the 2^0 position are represented the same as in figure 1. • The two digits in each of the position from 2^1 to 2^n are represented as shown for the 2^1 in figure 1.

10. DNA representation of all possible nonnegative two-digit binary integers

11. Generalization of the Algorithm • The resulting strand for larger n will be longer that that of our example, but the structure will be the same. • This generalized algorithm can readily be extended to the addition of any two n-digit positive rational numbers.

12. Operation • Addition is performed by combining in a test tube primer extension reagents plus the DNA strands appropriately representing the two numbers to be added, followed by a primer extension reaction.

13. Problems • Using the general algorithm to add two large binary numbers may require some technical modifications. • As the number of successive primer extension reactions increases, the possibility of errors in both these reactions and the readout process will increase • Only two numbers are added, so it does not take advantage of the massive parallel processing capabilities of DNA computing.

14. Problems • The first generation algorithm has another limitation. Because the output is encoded in a different form than the input, it is not presently possible to perform either iterative or parallel addition. • The algorithm described takes about 1 to 2 days of laboratory work to perform

15. Cryptography • Encryption - process of scrambling plaintext messages, transforming it into cipher text. • Decryption – transforming encrypted messages back into plaintext • Plaintext message encoded in DNA strands • Random One-Time Pad based schemes • Steganography Methods

16. Random One-Time Pad based schemes • Only systems known to be absolutely unbreakable • Use random codebooks which must only be used once to reduce risk of decryption • Random codebooks are used to convert short segments of plaintext messages to encrypted text • One time pads created in secret, and shared in advance by both sender and receiver

17. Cryptosystem Using Substitution • The input into this system is a plaintext binary message of length n • The message is then broken down into plaintext words of fixed length. • A substitution is then made from a one-time-pad that consists of a table randomly mapping all possible strings of plaintext words into cipher text. • It can also be done in reverse to decrypt.

18. Cryptosystem Using Substitution • The plaintext is encrypted by substituting each ith block of the plaintext with the cipher word given by the table.

19. One-time-pad Codebook DNA Sequence

20. DNA XOR Cryptosystem • XOR is the operation that given two Boolean inputs, yields 0 if the inputs are the same and 1 if they are different • If the plaintext message has a length of n, then a one-time-pad is made by randomly generating n bits. • One copy is stored in the source and one is stored in the destination.

21. DNA XOR Cryptosystem • Encryption: When a plaintext message M needs to be sent, each bit Mi is XOR’ed with bit Ki (randomly generated bit from the one-time-pad) to produce the encrypted bits Ci = Mi XOR’ed Ki (for I = 1, …n) • Once the plaintext message has been encrypted it is destroyed at the source. • The encrypted message is then sent to the destination. • Decryption: XOR the encrypted message with the same one-time-pad.

22. Steganography • Class of techniques that hide secret messages within other messages • Original plaintext is not encrypted but instead disguised or hidden in other data

23. Steganography Method • Takes one or more input DNA strands (considered to be the plaintext message) and appends to them one or more randomly constructed “secret key”. • The resulting “tagged plaintext” DNA strands are then hidden by mixing them within many other additional “distracter” DNA strands. Could also be constructed by random assembly. • Decryption: Given the “secret key” the strands can be decrypted by a number of possible know recombinant DNA separation methods.

24. Downside of Steganography • It is not unbreakable • If adversary know that there is an existence of a message, they will eventually decrypt the message. • It must also be difficult to distinguish the plaintext message from the “distracter” DNA.